First of all, decide what it is that you want to persuade your readers about. I suggest that you pick something that is fairly complex. For example, you don't want to pick a thesis statement such as, "Murder is wrong," because there really aren't two sides to the question. Thesis statements like "Abortion should be illegal," or "Social Security benefits should be improved by raising taxes on the rich" are much better, because there are most definitely two sides to these questions--even if you agree strongly with one of the sides.
Make a list of reasons that support the position that you are going to take. Also, make a list of some of the ideas that are put forth by those who disagree with your position.
Most of your essay should be about explaining your position and the reasons that you feel support it. However, you should also spend some "time" (perhaps one paragraph) disproving some of the arguments that are made by those who oppose your position.